7 November 2012

Mechanics Lab In this project, we have to have at least three different interactions, whether they are any sorts of movement, collisions, etc. I will now briefly explain to you my experimental design. First, a marble rolls down a roller-coaster, then slightly rolls up again, and flies off the track in projectile motion, which I called parts A and B. Next, as the marble flies, it lands into a cup that is taped onto a car. I called this parts B and C. This creates a perfectly in elastic collision. The momentum of the marble makes the car roll down a track and lands into a cup that is attached to an Atwood’s Machine. I called this parts C and D. Later, when the car lands into the cup that is attached to the Atwood’s Machine, its weight makes the whole cup go down and brings up the other side of the Atwood’s Machine, which has a small weight in it to keep the other side level to the track before the car lands in the cup. I called this part E. Continuing, when the opposite side of the Atwood’s Machine goes up, it hits below a level track with a ball on it. When it hits this track, the track rises at a certain angle, which creates torque, causing the ball to roll down the track. I called this parts F and G. Finally, when the ball is rolling down the ramp in parts F and G, it rolls right off of the track and into a cup placed a certain distance away from the track. I called this part H. In smaller words, using different theorems and equations, I had to calculate how far a cup should be placed away from the ramp so that the ball would land into the cup when rolled off of a ramp after many interactions and compare the distance to an actual trial to see how accurate our results were. Attached is a diagram of my experimental set-up that will help you better understand what exactly has to be done and calculated. To theoretically determine how far I needed to place the cup away from the track, I needed to use many different theorems and equations. First, by using potential energy and kinetic energy of the marble, I can calculate the maximum distance the marble will go on the angle created by the track so that I know how far and how high to place the car with the cup attached to it. Please refer to the calculations for parts A-B on page 5. Next, with knowing the height of the track and the mass of the marble, we were able to calculate the velocity of the marble when it comes off of the track so that we can use that for our equation for parts B-C. Later, we were able to use the velocity calculated in the previous section to determine the speed of the car going down the track, since it was a perfectly inelastic collision. This is parts C-D on the calculations sheet. Eventually, the car would roll down the track and fall into a cup attached to an Atwood’s Machine. Next, using the masses of the weight and the car, we were able to solve for the acceleration of the Atwood’s machine when the car falls into the cup. This is illustrated by parts D-E on the calculations sheet and the diagram. In addition, due to the acceleration of the Atwood’s Machine, it created torque on the track, as it raised the track since the track was attached to the side of the Atwood’s Machine with the weight on it. We knew the angle was 90…